This cost function has a tendency to split small sets of objects, since the cost increases with the number of inter-cluster edge weights, i.e., the edges connecting the different clusters. Figure REF  illustrates such a situation for two clusters [1]}. We assume that the edge weights are inversely proportional to the distances between the objects. It is observed that Min Cut favors splitting objects \(i\)  or \(j\) , instead of performing a more balanced split. In fact, any cut that splits one of the objects on the right half will yield a smaller cost than the cut that partitions the objects into the left and right halves. This issue is particularly problematic when the intra-cluster edge weights are heterogeneous among different clusters.
Thus, several methods propose to normalize the Min Cut clusters by a cluster depending factor, e.g., the size of clusters (Ratio Assoc [2]} and Ratio Cut [3]}) or the degree of clusters (Normalized Cut [1]}).
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